Block-Term Tensor Decomposition: Model Selection and Computation

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed blocks rank higher than one, a scenario encountered in numerous diverse applications. Its uniqueness approximation have thus thoroughly studied. Nevertheless, the challenging problem estimating BTD structure, namely number block terms their individual ranks, only started attract significant attention. In this paper, novel method selection computation is proposed, based on idea imposing column sparsity xmlns:xlink="http://www.w3.org/1999/xlink">jointly factors xmlns:xlink="http://www.w3.org/1999/xlink">hierarchical manner ranks as numbers factor columns non-negligible magnitude. Following successive upper bound minimization (BSUM) approach for proposed optimization shown result an alternating hierarchical iteratively reweighted least squares (HIRLS) algorithm, which fast converging enjoys high computational efficiency, it relies iterations small-sized sub-problems with closed-form solutions. Simulation results both synthetic examples hyper-spectral image denoising application reported, demonstrate superiority scheme over state-of-the-art success rate estimation well time convergence while attaining comparable performance.